# How do you use the properties of logarithms to expand lnz(z-1)^2?

Sep 4, 2017

$\ln z + 2 \ln \left(z - 1\right)$

#### Explanation:

$\text{using the "color(blue)"laws of logarithms}$

•color(white)(x)logx+logyhArrlog(xy)

•color(white)(x)logx^nhArrnlogx

$\Rightarrow \ln z {\left(z - 1\right)}^{2}$

$= \ln z + \ln {\left(z - 1\right)}^{2}$

$= \ln z + 2 \ln \left(z - 1\right)$